Some fringe parties including CPN-Maoist, the breakaway faction of Unified CPN-Maoist, and its allies have been demanding his resignation as the Chief Justice of the Supreme Court to ensure a conducive environment for the November 19 parliamentary elections.
Regmi has been holding both the posts since March 13.
A case had been filed in the Supreme Court by lawyer Bharat Jungam demanding Regmi's resignation as Chief justice.
In a written reply to the Supreme Court yesterday, Regmi said that there was a provision in the Constitution that the government would be headed by a sitting Chief Justice in special circumstances.
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Besides CPN-Maoist opposition parties Madhesi Peoples Forum Nepal, and the Federal Socialist Party-Nepal are demanding Regmi's resignation as Chief Justice, saying that holding both posts by an individual will affect the principle of separation of powers.
Regmi in his reply also cited examples in Greece, Canada and Ghana, arguing that sitting Chief Justices have assumed executive roles.
The apex court had last month asked Regmi to explain why he was holding both the positions.
After the dissolution of the constituent assembly in May last year, Nepal had plunged into serious political and constitutional crisis as parties failed to agree on a constitution.
The political deadlock broke after Regmi was appointment as the country's new Prime Minister to head an interim government to hold elections to the 601-member constituent assembly.